Cheap control tracking performance for non-right-invertible systems

There exists a well-known fundamental limitation upon the achievable setpoint tracking performance of a non-right-invertible plant. This limitation manifests itself, for example, in the cost associated with the cheap control tracking problem. In this paper, we provide a new interpretation of this limitation. We show that the cheap control cost may be decomposed into the sum of two terms. The first of these depends upon certain non-minimum phase zeroes that include the non-minimum phase plant zeroes. The second term depends upon the extent to which the plant direction varies with frequency. To state these results, we first develop a co-ordinate transformation that may be used to define the notion of frequency dependent plant direction and to display the relevant non-minimum phase zeroes. We also show that the cheap control cost is connected to an integral relation that constrains the performance of any stable closed-loop system (not necessarily under cheap control) for which the plant has a single control input and two performance outputs. Copyright © 2002 John Wiley & Sons, Ltd.

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